Question 123232
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<h3 style="font: bold times">
Discussion
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<p style="font: courier">
To solve a system of linear equations by substitution, you first solve one
of the equations for one of the variables to get an expression for that 
variable in terms of the other.  Then you substitute this expression into the 
second equation giving you a single equation in a single variable that can be
solved by ordinary methods
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<h3 style="font: bold times">
Solution
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{{{x+2y=13}}}
{{{3x-5y=6}}}


Solve the first equation for x:
{{{x+2y=13}}}
Add -2y to both sides
{{{x=13-2y}}}


Take this expression for x and substitute it into the second equation:
{{{cartoon(3*red(x)-5y=6,3*red((13-2y))-5y=6)}}}


Now solve:
{{{3(13-2y)-5y=6)}}}
{{{39-6y-5y=6}}}
{{{-11y=6-39}}}
{{{-11y=-33}}}
{{{y=3}}}


Now that you know the value of y, you can substitute it into either of the
original equations and solve for x
{{{x+2(3)=13}}}
{{{x+6=13}}}
{{{x=7}}}


So the solution set for the system is the ordered pair (7,3)

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Check Answer
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<p style="font: courier">
{{{graph(400,400,-10,10,-10,10,-x/2+13/2,3x/5-6/5)}}}


Note that the two lines intersect at the point (7,3)
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